This work applies a projection-based model-reduction approach to make high-order quadrature (HOQ) computationally feasible for the discrete ordinates approximation of the radiative transfer equation (RTE) for purely absorbing applications. In contrast to traditional discrete ordinates variants, the proposed method provides easily evaluated error estimates associated with the angular discretization as well as an efficient approach for reducing this error to an arbitrary level. In particular, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model (ROM) constructed from this reduced basis. This strategy results in a much more accurate solution than might have been achieved using only the ordinate directions used to construct the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.
Skip Nav Destination
Article navigation
December 2017
This article was originally published in
Journal of Heat Transfer
Research-Article
Accelerated Solution of Discrete Ordinates Approximation to the Boltzmann Transport Equation for a Gray Absorbing–Emitting Medium Via Model Reduction
Roy Hogan
Roy Hogan
Search for other works by this author on:
John Tencer
Kevin Carlberg
Marvin Larsen
Roy Hogan
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 31, 2017; final manuscript received June 12, 2017; published online August 1, 2017. Assoc. Editor: Ravi Prasher.
J. Heat Transfer. Dec 2017, 139(12): 122701 (9 pages)
Published Online: August 1, 2017
Article history
Received:
January 31, 2017
Revised:
June 12, 2017
Citation
Tencer, J., Carlberg, K., Larsen, M., and Hogan, R. (August 1, 2017). "Accelerated Solution of Discrete Ordinates Approximation to the Boltzmann Transport Equation for a Gray Absorbing–Emitting Medium Via Model Reduction." ASME. J. Heat Transfer. December 2017; 139(12): 122701. https://doi.org/10.1115/1.4037098
Download citation file:
Get Email Alerts
Cited By
Related Articles
On Multilayer Modeling of Radiative Transfer for Use With the Multisource k-Distribution Method for Inhomogeneous Media
J. Heat Transfer (June,2014)
Effects of Radiative Transfer Modeling on Transient Temperature Distribution in Semitransparent Glass Rod
J. Heat Transfer (August,2003)
On the Entropy Generation Formula of Radiation Heat Transfer Processes
J. Heat Transfer (May,2006)
Numerical Simulation and Convergence Analysis of Fractional Optimization Problems With Right-Sided Caputo Fractional Derivative
J. Comput. Nonlinear Dynam (January,2018)
Related Proceedings Papers
Related Chapters
Fitting a Function and Its Derivative
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17
On the Exact Analysis of Non-Coherent Fault Trees: The ASTRA Package (PSAM-0285)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
CMA1-2 Based on Coordinate Transformation
International Conference on Electronics, Information and Communication Engineering (EICE 2012)